Need help on part (d) and (e) 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases but labour supply decreases. Using the concept of the marginal rate of substitution, explain why this is a likely outcome. e) Now assume that, starting from the optimal point in d), your wage increases to £18 per hour. Explain why the impact of this change is ambiguous, and relate to the long-run historical experience of wage growth in rich countries.
Need help on part (d) and (e)
6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income.
a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes).
b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference
c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day.
d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases but labour supply decreases. Using the concept of the marginal rate of substitution, explain why this is a likely outcome.
e) Now assume that, starting from the optimal point in d), your wage increases to £18 per hour. Explain why the impact of this change is ambiguous, and relate to the long-run historical experience of wage growth in rich countries.
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